Time-of-flight of solitary waves in dry and wet chains of beads: Experimental results and phenomenological models

A highly nonlinear solitary wave is generated by impacting a dry chain of beads on one of its ends. Its speed depends on the speed $v0$ of the striker and the details of the contact force. The force on the bead at the site n = 7 and the end of the chain, as well as the time-of-flight (ToF) of both, the incident and reflected waves, is measured as a function of $v0$⁠. This study was performed on a chain of stainless steel beads in two general cases: the dry chain and wet chains having three different types of oil on and around the contact points between the beads. The ToF displays a complex dependence on the fluid’s rheological properties not seen in previous studies. Power-law dependencies of the ToF on $v0$ in both, dry and wet, cases were found. It turned out that the Hertz plus viscoelastic interactions are not enough to account for the measured data. Two phenomenological models providing a unified and accurate account of our results were developed.